Proceedings of the World Congress on Engineering 2013 Vol III,
WCE 2013, July 3 - 5, 2013, London, U.K.
Air Flow Optimization via a Venturi Type Air
Restrictor
Anshul Singhal, Mallika Parveen, Member, IAENG

Abstract— The aim of this project is to create a flow
restriction device to be fitted in the FSAE (Formula Society of
Automotive Engineers) car being built by Team Gear Shifters
of BITS-Pilani, Dubai. The car is an open-wheeled race vehicle,
designed to go from 0-100 kmph in under 4 seconds and have a
top speed of about 140kmph. In order to comply with the rules
of the competition imposed by FSAE, a single circular
restrictor of 20mm diameter must be placed in the intake
system between the throttle and the engine and all engine
airflow must pass through the restrictor. This is done
primarily to limit the power capability from the engine. Since
the maximum mass flow rate is now a fixed parameter because
of the restrictor, the aim is to allow the engine to achieve the
maximum mass flow with minimal pull from the engine. In
short, the pressure difference between atmosphere and the
pressure created in the cylinder should be minimal, so that
maximum airflow into the engine at all times. From the data
gathered through the numerous simulations in SolidWorks
Flow Simulation, it can be observed that the optimized values
for converging angle and diverging angle of the Venturi were
found to be 18 degrees and 6 degrees respectively.
Index Terms— Air Flow, Design Optimization, FSAE Air
Restrictor, SolidWorks Flow Simulation
T
I. INTRODUCTION
HE aim of this project is to create a flow restriction
device to be fitted in the FSAE (Formula Society of
Automotive Engineers) car being built by Team Gear
Shifters of BITS-Pilani, Dubai Campus. The car is an openwheeled race vehicle, designed to go from 0-100 kmph in
under 4 seconds and have a top speed of about 140kmph. In
order to comply with the rules of the competition imposed
by FSAE, a single circular restrictor of 20mm diameter must
be placed in the intake system between the throttle and the
engine and all engine airflow must pass through the
restrictor. This is done primarily to limit the power
capability from the engine [10].
An Internal Combustion Engine takes in air from the
environment and the air-fuel mixture is combusted inside
the engine cylinders to generate the power required to run
Manuscript received March 24, 2013; revised April 10, 2013.
Anshul Singhal is with the Birla Institute of Technology and Science
Pilani, Dubai Campus; Dubai International Academic City, PO BOX –
345055
UAE;
phone:
+971
555
531826;
e-mail:
anshulsinghal33@gmail.com
Mallika Parveen is with the Birla Institute of Technology and Science
Pilani, Dubai Campus; Dubai International Academic City, PO BOX –
345055 UAE; phone: +971 508 412493; e-mail: parveen@bits-dubai.ac.ae
ISBN: 978-988-19252-9-9
ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
the vehicle. In a naturally aspirated engine, the engine
creates a low pressure during the intake stroke, causing the
air from the atmosphere to enter the cylinders [2]. The
higher the rpm, the greater the pull, and the lower the
pressure created inside the cylinder. According to the
stoichiometric air-fuel ratio, to burn 1 gram of gasoline 14.7
grams of air is required. By reducing the diameter of the
flow path from 50mm to 20mm, the flow cross-section area
has reduced drastically [11]. At low rpm’s of the engine
when the engine requires less air, the reduction in area is
compensated by the accelerated flow of air through the
throat (20mm section). But since the car is designed to run
at high rpm’s (6,000rpm to 10,000rpm with the restrictor
attached), the flow at the throat reaches sonic velocities
(also known as Critical Flow condition), and therein lays the
problem. Critical Flow exists when the mass flow is the
maximum possible for the existing upstream conditions, and
the average velocity closely approximates the local sonic
velocity (speed of sound in air ≈ 330m/s, or Mach 1) [3].
Since the maximum mass flow rate is now a fixed parameter
because of the restrictor, the aim is to allow the engine to
achieve the maximum mass flow with minimal pull from the
engine. In short, the pressure difference between
atmosphere and the pressure created in the cylinder should
be minimal, so that maximum airflow into the engine at all
times.
II. METHOD OF RESEARCH
A. Deciding an Appropriate Kind of Obstruction Meter
Air Restrictor that is being designed is basically a kind of
an Obstruction Meter. Since the aim is to optimize the Mass
Flow rate we will first study different kinds of Obstruction
Meters available. Broadly there exist two obstruction meters
used in industries – Orifice and Venturi meters.
a. Orifice.
An orifice plate is a thin plate with a hole in the
middle. It is usually placed in a pipe in which fluid flows.
When the fluid reaches the orifice plate, the fluid is forced
to converge to go through the small hole; the point of
maximum convergence actually occurs shortly downstream
of the physical orifice, at the so-called vena contracta point.
As it does so, the velocity and the pressure change. Beyond
the vena contracta, the fluid expands and the velocity and
pressure change once again. By measuring the difference in
fluid pressure between the normal pipe section and at the
vena contracta, the volumetric and mass flow rates can be
WCE 2013
Proceedings of the World Congress on Engineering 2013 Vol III,
WCE 2013, July 3 - 5, 2013, London, U.K.
obtained from Bernoulli’s equation. It generally has a
Coefficient of drag around 0.65 [7]
b. Venturi.
The Venturi tube or simply a Venturi is a tubular setup
of varying pipe diameter through which the fluid flows. It
follows the same laws as the orifice meter (for compressible
fluids, the velocities have to be subsonic). The Venturi
effect is a jet effect; as with a funnel the velocity of the fluid
increases as the cross sectional area decreases, with the
static pressure correspondingly decreasing [4]. According to
the laws governing fluid dynamics, a fluid’s velocity must
increase as it passes through a constriction to satisfy the
principle of continuity, while its pressure must decrease to
satisfy the principle of conservation of mechanical energy.
Thus a drop in pressure negates any gain in kinetic energy a
fluid may accrue due to its increased velocity through a
constriction. An equation for the drop in pressure due to the
Venturi effect may be derived from a combination of
Bernoulli’s principle and the continuity equation. It
generally has a coefficient of drag around 0.85 [8].
Inference:
After analysing the two kinds of obstruction meters
available it can be concluded that the appropriate
obstruction meter for designing the Air restrictor would be
Venturi meter with Cd (~0.85), which is greater than the Cd
(~0.65) of Orifice meter.
B. Deciding the Parameter to Be Optimized
The main objective of using the Venturi design in the air
restrictor is to maintain a constant mass flow rate with
optimum flow of air. The mass flow rate can be maintained
constant by varying any one of the parameters namely a. Energy
b. Velocity
c. Mach number
d. Pressure.
For practical applications calculating the Energy, Mach
number and Velocity is an intricate process. Mach number
is calculated using the equation:
M=
v
a
(1)
Where,
M is the Mach number,
v is the velocity of the source relative to the medium and
a is the speed of sound in the medium.
III. THEORY AND FORMULAE
For this we use theoretical data and formulae of the
Venturi meter in the following way. Using Bernoulli’s
equation in the special case of incompressible flows (e.g.
the flow of water or other liquid, or low speed flow of gas
v), the theoretical pressure drop p1-p2 at the constriction is
given by [13]:
p1  p2 
Where,


2
(v22  v12 )
(2)
is the density of air.
Volumetric flow rate Q is given by: -
Q  v1 A1  v2 A2
(3)
Where A the area of cross-section of Venturi at any point
and v is the velocity of air at that point.
p1  p2 

2
(v22  v12 )
(4)
Then
Q  A1
2 ( p1  p2 )
2 ( p1  p2 )

 A2

2
2
  A1 

A2 
1
1
 
 
A2 
 A1 
(5)
But as we can see, all the above calculations have been
made based on one assumption – Incompressible Flow.
Unfortunately, the fluid under observation is Air, and air is
compressible, meaning that we have to take the
compressible part of air into account. To derive the equation
for Mass Flow Rate of an Ideal Compressible Fluid, we
have to go back to the basics [10].
The conservation of mass is a fundamental concept of
physics. Within some problem domain, the amount of mass
remains constant; mass is neither created nor destroyed. The
mass of any object is simply the volume that the object
occupies times the density of the object. For a fluid (a liquid
or a gas) the density, volume, and shape of the object can all
change within the domain with time and mass can move
through the domain [1].
When the medium is changed the velocity of sound in the
medium will change accordingly and knowing the exact
value for it is difficult. Due to this using velocity and Mach
number as a parameter in a fixed Venturi apparatus is not
feasible. For a permanent installation of air restrictor it is
tedious and impracticable to deal with the above parameters
for an optimum result.
The conservation of mass (continuity) tells us that the
mass flow rate through a tube is a constant and equal to the
product of the density ρ, velocity V, and flow area A:
Inference:
Pressure is the most ideal parameter that can be varied to
hold the flow rate constant because pressure difference
across the two ends of a Venturi can be measured easily
using a simple U-shaped manometer [9].
the mass flow rate indefinitely by simply increasing the
velocity v. In real fluids, however, the density does not
remain fixed as the velocity increases because of
compressibility effects. We have to account for the change
ISBN: 978-988-19252-9-9
ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
m=ρ*V*A
(6)
Considering the mass flow rate m equation, it appears that
for a given area A and a fixed density  , we could increase
WCE 2013
Proceedings of the World Congress on Engineering 2013 Vol III,
WCE 2013, July 3 - 5, 2013, London, U.K.
in density to determine the mass flow rate at higher
velocities. If we start with the mass flow rate equation given
above and use the isentropic flow relations and the equation
of state, we can derive a compressible form of the mass flow
rate equation. We begin with the definition of the Mach
number M and the speed of sound a [12]-[5]:
V = M * a = M * sqrt (γ * R * T)
(7)
Where γ is the specific heat ratio, R is the gas constant,
and T is the temperature.
Now substitute (7) into (6):
m = ρ * A * M * sqrt (γ* R * T)
(8)
The equation of state is:
ρ = P / (R * T)
(9)
Where P is the pressure. Substitute (9) into (8):
m = A * M * sqrt (ρ* R * T) * P / (R * T)
(10)
m = A * sqrt (γ/ R) * M * P / sqrt(T)
(11)
(12)
Where Pt is the total pressure and Tt is the total
temperature. Substitute (12) into (11):
m = (A * Pt) / sqrt(Tt) * sqrt (γ/ R) * M * (T / Tt)^(( γ + 1)
/ (2 * (γ -1 )))
(13)
Another isentropic relation gives:
T/ Tt = (1 + .5 * (γ-1) * M^2) ^-1
(14)
Substitute (14) into (13):
m = (A * Pt/sqrt[Tt]) * sqrt(γ /R) * M * [1 + .5 * (γ -1) *
M^2 ]^-[( γ + 1)/( γ - 1)/2]
(15)
This equation is shown in the red box below (NASA). It
relates the mass flow rate to the flow area A, total pressure
Pt and temperature Tt of the flow, the Mach number M, the
ratio of specific heats of the gas γ, and the gas constant R.
ISBN: 978-988-19252-9-9
ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
The values taken for substitution in Equation #10 are:
Pt = 101325 Pa
T = 300K
 = 1.4
R (air) =0.286 kJ/Kg-K
A = 0.001256 m2
M = 1 (Choking Conditions)
Result: Mass Flow Rate at Choking = 0.0703 kg/s
IV. DATA ANAYLSIS
From the isentropic flow equations:
P = Pt * (T / Tt)^(γ/(γ-1))
Fig 1. Formulae for Mass Flow Choking [9]
Calculations:
A. Aim
To maximise pressure recovery at outlet
B. Variables
a. Dependent Variables:
Delta Pressure (= Inlet Pressure – Outlet
Pressure)
b. Independent Variables:
Converging angle and Diverging angle
c. Constants:
Inlet, Outlet and Throat diameter, Type of Fluid
-Air, Temperature - 300K
C. Boundary Conditions
a. Inlet Face: Total Pressure = 1 bar
b. Outlet Face: Mass Flow Rate = 0.0703kg/s
D. Software Used
1. Modelling
2. Analysis
3. Data Tabulation
4. Data Interpretation
5. Data Compilation
6. Paper Formatting
- CATIA V5
- SolidWorks 2012-2013
- MS Excel 2007
- MATLAB
- MS Word 2007
- Adobe InDesign
WCE 2013
Proceedings of the World Congress on Engineering 2013 Vol III,
WCE 2013, July 3 - 5, 2013, London, U.K.
E. Data Collection and Analysis
Table I. Delta Pressure for Different Converging and
Diverging Angles
Inference:
From the table and graph above, it can be seen that Delta
Pressure keeps increasing after 18 degrees as the
Converging Angle increases. It is inferred that the Minimum
value for Delta Pressure is achieved when the Converging
Angle is 18 degrees and the Diverging Angle is 6 degrees.
F. Images of Data Analysis in Solid Works 2012-13
For the calculated Maximum Mass Flow Rate of 0.0703
kg/s, the Delta Pressure (Inlet Pressure – Outlet Pressure)
was calculated for different converging and diverging
angles. The minimum angle that can be manufactured with
considerable precision was estimated at 4 degrees, hence the
diverging angle has been considered from 4 degrees. The
Diverging angle range was considered until 20 degrees
because the value of Delta Pressure was increasing abruptly
after 15 degrees, clearly visible by the lack of any minimum
value in the 20 degrees columns. The Converging Angles
have been considered from 10 degrees referring to the
estimates of Venturi designs previously made [6].
In the Data collected the Minimum Delta Pressure Value
was marked for every row and column as shown in the table
above to find out the best combination of Diverging and
Converging angle. From the above table, we can see that
most of the minimum values are achieved when the
Diverging Angle is 6 degrees. Therefore we shall
concentrate on 6 degrees as the Diverging Angle and extend
our testing to Converging Angles of 22 degrees and 25
degrees, also because a persistent trend was lacking. The
data for Diverging Angle of 6 degrees is shown below [2].
Table II. Table of Delta Pressure for Diverging Angle of
6 Degrees
Fig 2. Pressure variation – Converging angle 18 degrees
and Diverging angle 6 degrees
Fig 3. Density Variation – Converging Angle 18 Degrees
and Diverging Angle 6 Degrees
Fig 4. Velocity Variation – Converging Angle 18
Degrees And Diverging Angle 6 Degrees
ISBN: 978-988-19252-9-9
ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
WCE 2013
Proceedings of the World Congress on Engineering 2013 Vol III,
WCE 2013, July 3 - 5, 2013, London, U.K.
REFERENCES
V. CONCLUSION
The optimum solution to achieve maximum possible mass
flow rate of air as quickly as possible is to minimize the
pressure loss through the flow restriction device. The best
general design for this objective is to use the Venturi design.
From the data gathered through the numerous simulations, it
can be observed that the values for converging angle and
diverging angle of the Venturi are 18 degrees and 6 degrees
respectively.
FSAE is about speed, acceleration and economy. Therefore
a majority of the parts that need to be fabricated for the
FSAE car are made using sheet metal. Also procuring a
billet of diameter greater than 50 mm and the subsequent
machining of the part to our specifications using a lathe was
significantly more difficult and expensive, and so it was
finalised that sheet metal will be used. Galvanised iron
sheets were beaten into their respective profiles, welded,
primer and spray-painted. The total cost borne was AED 15
for the primer coat and the spray paint; the sheet metal and
welding services were borrowed from the Mechanical
Workshop of the College.
The manufactured restrictor serves the purpose of
complying with the rules with minimal compromise on
power. As soon as the effective vacuum pressure created by
the suction strokes of the engine cylinders reaches
≈17800Pa, maximum mass flow rate is achieved and
subsequently maximum power of the engine as well (for the
same rpm using any other restrictor specification).
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
Abdulnaser Syma, “Computational Fluid Dynamics,” 1st edition.
Available:http://bookboon.com/en/textbooks/energyenvironment/com
putational-fluid-dynamics
Anish Ganesh, “Students Win Using Simulation-Driven Design,”
University of Waterloo Formula Motorsports, Canada. Available at:
http://www.idac.co.uk/enews/articles/Students-Win-Using-SimDriven-Design.pdf
Antonio Gomes, “Documentation of the Engine Design Process for
FSAE,” Department of Mechanical and Industrial Engineering
University
of
Toronto,
March
2007.
Available
at:
http://www.studymode.com/essays/The-Anlyse-Of-Intake1258959.html
ASME MFC-7M, Measurement of Gas Flow by Means of Critical
Flow Venturi Nozzles. New York: American Society of Mechanical
Engineers; 1987.
Bean, H. S., ed. Fluid Meters: Their Theory and Application, 5th
edition. New York: The American Society of Mechanical Engineers;
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Deepak Ranjan Bhola, “CFS Analysis Of Flow Through Venturi Of A
Carburetor,” National Institute of Technology Rourkela, Rourkela –
769008,
India,
May
2011.
Available
at:
http://ethesis.nitrkl.ac.in/2296/1/final_report.pdf
Orifice Plate description – Flow through an Orifice, Available at:
en.wikipedia.org/wiki/Orifice_plate, Consulted on – 2 Feb 2013
Venturi description – Flow through a Venturi Available at:
en.wikipedia.org/wiki/Venturi_effect, Consulted on – 20 Jan 2013
www.grc.nasa.gov/WWW/k-12/airplane/mflchk.html, Consulted on –
15 Feb 2013
Neal Persaud, “Design and Optimization Of a Formulae SAE Cooling
System,” Department of Mechanical and Industrial Engineering,
University
Of
Toronto,
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Available
at:
http://docsse.com/view.php?id=856504
FSAE Variable Air Intake Consulted on – 22 JAN 2013
http://poisson.me.dal.ca/~dp_06_9/concept.htm
Section 8, “Sonic Flow Nozzles and Venturi — Critical Flow, Choked
Flow Condition”, ASME Publication
Jack Philip Holman, Experimental Methods for Engineers 6th edition,
September 1993, McGraw-Hill Higher Education
ACKNOWLEDGMENT
I would like to thank all the people who contributed their
time and helped me in writing this paper and completing in
timely manner. I would also thank them for making this
paper a successful one.
I would like to thank Dr. R.K. Mittal, BPD Director, for
giving me the opportunity to take up this paper. I would also
like to extend my gratitude to my friends and senior students
of this department who have always encouraged and
supported in doing my work. Last but not the least I would
like to thank all the staff members of Department of
Mechanical Engineering who have been very cooperative
with me. I would like to make a special note of thanks to Dr.
Mallika Parveen for her constant guidance and supervision
in all respects of this paper.
ISBN: 978-988-19252-9-9
ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
WCE 2013